The backgammon world has been changed forever by the arrival of strong neural net backgammon programs, or “bots”, which play the game at a very high level. The best of these is Extreme Gammon, but there are a number of others that also play well, if not quite infallibly.

In this post, I’ll discuss some of these changes, with particular attention to the curious fact that all of the better bots are routinely accused of cheating.

Backgammon playing bots use much the same technique as computerized players in chess or other games. They have an evaluation function that assesses the equity of any particular position. On its least skillful setting, it simply chooses among the legal moves the one that maximizes this function. On higher settings, it looks further ahead, considering its opponent’s response for each of the 25 different dice throws. At a still higher level, it takes the process one step further, analyzing the 25 possible dice throws for its own next move. And so forth, up to some practical limit – the number of possible continuations grows so rapidly that it cannot look ahead more than four or five of these plies.

The computer’s play is not infallible – I sometimes enjoy setting up a position in that it doesn’t understand because it can’t see far enough ahead. But, as a practical matter, computer analysis is good enough that in all ordinary positions its evaluation is correct. And this has affected the way people play the game. Now, questions that have engaged players for years have answers. There’s a cottage industry, represented by the book Classic Backgammon Revisited, in finding the errors in the leading backgammon books from before the computer revolution.

Leading players now routinely practice by playing against the computer, studying carefully any discrepancy between the machine’s judgment and the player’s own. It’s a testament to the difficulty of the game that it’s often very difficult to understand why the computer’s move is better.

Cheating

In the hands of a casual player, bots are used (and abused) very differently. The casual player simply wants an opponent when no human being is available. And many casual players (even some who play reasonably well) are convinced that the programs don’t play fair.

It would, of course, be easy to program a computer to cheat. The computer is in charge of the dice, and could give itself better rolls than it gives the player. But even if it didn’t alter the roll of the dice, if it looked ahead to see what the roll was going to be, it could make moves that take advantage of the luck that is to come.

But computers don’t need to cheat – they can beat most human players without it. In fact, one of the weaknesses of bots is that they don’t know how to play a bad game. Most of them have settings that allow the user to specify an unskillful opponent, but the mistakes that the bots make on such settings are nothing like the mistakes that humans make.

Developers are, understandably, irritated by the accusations of cheating. The programs almost all have a setting allowing the user to roll real dice, though this is a silly way to play. They compile tables to show that the distribution of dice rolls is as expected, and allow the user to reset the seed of the random number generator so that they can see that the same dice rolls will come up regardless of the position on the board. It’s really rather easy to show that the programs do not cheat, or at least, do not cheat in the way that users think they do.

It’s not surprising that casual players are tempted to think the computer is cheating. If it’s difficult for advanced players to understand why the computer makes moves that look wrong to them, it’s all the more likely that computer moves look wrong to the casual player. The repeated experience is to see a computer doing things that look silly, and winning anyway. Something must be fishy.

But it’s remarkable how virulent the complaints against the computer are, and how very resistant they are to contrary evidence. It doesn’t occur to the doubters to wonder what reason a developer could possibly have for programming a computer to cheat. They experience their losses to the bloodless machine as a personal affront. They seem to assume, without much thought, the idea that the developer is reaping some sort of material reward from unjustly making them feel stupid.

We have only to look at the results of the last U.S. presidential election to see how common it is for people to embrace the idea that some cabal of insiders is manipulating things to make it appear that obvious truths are untrue, and that their deepest intuitions are not to be trusted.

Ironically, the bots have, indeed, increased the amount of cheating in the backgammon world. But it is humans rather than computers that are cheating. Playing online, especially for money, is hazardous these days, as there’s always a chance that the opponent is running one of the bots, and is using it to play better. The proprietors of some online backgammon sites run bots in the background, trying to root out cheating by identifing players whose decisions are too bot-like.